Question: Given $ m \angle ABC = 4x + 39$, and $ m \angle CBD = 3x + 92$, find $m\angle ABC$. $B$ $A$ $D$ $C$
From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {4x + 39} + {3x + 92} = {180}$ Combine like terms: $ 7x + 131 = 180$ Subtract $131$ from both sides: $ 7x = 49$ Divide both sides by $7$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $m\angle ABC$ $ m\angle ABC = 4({7}) + 39$ Simplify: $ {m\angle ABC = 28 + 39}$ So ${m\angle ABC = 67}$.